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AP EAMCET202018 Sep 2020Evening ShiftMathematicsStraight LinesActual

When the origin is shifted to ((2,3) ) the transformed equation (x^2+3 x y-2 y^2+17 x-7 y-11=0 ), then the original equation of curve is

Options

  1. A(x^2-2 y^2-3 x y+4 x-y+20=0 )
  2. B(x^2-2 y^2+3 x y+4 x-y-20=0 )
  3. C(x^2-2 y^2-3 x y-4 x-y+20=0 )
  4. D(x^2-2 y^2-3 x y+4 x-y-20=0 )

Correct answer

B. (x^2-2 y^2+3 x y+4 x-y-20=0 )

Step-by-step solution

It is given that the origin is shifted to point ((2,3) ) and due to that the transformed equation of the curve is, (x^2+3 x y-2 y^2+17 x-7 y-11=0 ), to get the original equation of curve, replace ((x, y) ) by ((x-2, y-3) ), so by doing this. we get, ((x-2)^2+3(x-2)(y-3)-2(y-3)^2 ) ( gathered +17(x-2)-7(y-3)-11=0 x^2-4 x+4+3(x y-3 x-2 y+6)-2 (y^2-6 y+9 ) +17 x-34-7 y+21-11=0 x^2+3 x y-2 y^2+4 x-y-20=0 gathered ) Hence, option (b) is correct.

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